The team has won the most Memorial Cups of any team in the WHL with five cups; two as New Westminster (1977 and 1978) and three as Kamloops (1992, 1994 and 1995). The CHL record is seven cups, held by the Toronto Marlboros, who are now the Guelph Storm.

The franchise began in 1946 as the Humboldt Indians of the Saskatchewan Junior Hockey League and moved to Estevan to become the Bruins in 1957. The franchise has won the President's Cup a record eleven times: once in Estevan, four times in a row in New Westminster and six times since coming to Kamloops. The Blazers hosted the 1995 Memorial Cup, although they went in the "front door" by also winning the WHL championship that year.